The present invention relates generally to techniques for bending planar surfaces and more particularly to a specific technique for correcting for astigmatism in a light beam reflected off of a light reflecting surface by adjustably bending the surface in a selected manner.
It is not uncommon for astigmatism to develop in a light beam passing through an optical system. A known way to correct for this astigmatism is to reflect the beam off of a mirrored surface which has a slight convex or concave cylindrical configuration in the appropriate direction relative to the incident axis of the beam's astigmatism. The degree of curvature depends upon the amount of astigmatism in the beam. FIG. 1 illustrates means 10 defining a cylindrical light reflecting surface 12 having a radius of curvature r. The axis of the cylinder including surface 12 extends normal to the axis of the incident beam 14 (into the plane of the paper). The degree of curvature of surface 12, that is, the size of radius r, and whether the surface is convex relative to the incoming beam as illustrated by solid lines or concave (as shown by dotted lines), depends upon the amount of astigmatism in beam 14 which is to be corrected (if at all). If the beam displays no astigmatism at all, surface 12 would be entirely flat.
The discussion of FIG. 1 immediately above assumes that the astigmatism in beam 14 could be predetermined. As a result, means 10 defines a fixed surface 12. In some cases, it is not possible to predetermine the astigmatism to be corrected for and therefore it is not possible to provide the appropriately curved light reflecting surface ahead of time. In FIG. 2 there is illustrated an apparatus generally indicated by the reference numeral 16 for adjustably bending a light reflecting surface 18 into a particular cylindrical shape whose radius can be selected depending upon the astigmatism to be corrected. As seen in FIG. 2, the surface 18 is defined by a bendable plate like member 20 including rearwardly extending spaced-apart ribs 22, 24 and 26. The apparatus also includes a mechanism 28 including gripping members 30, 32 and 34 for gripping ribs 22, 24, and 26, respectively, in order to support the overall plate like member in the position illustrated. The upper and lower gripping members 30 and 34 are fixed and therefore retain the ribs 22 and 26, and therefore the upper and lower edges of surface 18, in fixed positions. At the same time, gripping member 32 is movable back and forth, to a limited extent, in the direction of two way arrow 36, that is, normal to surface 18 and along a line through the center of the light reflecting surface. Means including the motor 38 or any other suitable drive mechanism is provided for moving the gripping member 32 in the manner just recited, in a controlled fashion, in order to bend surface 18 to a desired curvature depending upon the amount of astigmatism of the light beam being reflected off of surface 18. FIG. 3 diagrammatically illustrates the way in which plate 20 is acted upon in order to bend surface 18.
The overall apparatus 16 just described is known in the art. While such an apparatus provides an in line technique for adjusting the curvature of a light reflecting surface for astigmatism, the push-pull approach utilized does not result in a purely cylindrical shape that is, in mathematical terms, proportionate to X.sup.2 (for small curvatures) where X is measured perpendicular to the cylinder's axis in the plane of the reflecting surface. Rather, the push-pull action at the center of the surface to be bent, as in the apparatus illustrated in FIG. 2, produces a sizeable term, generally proportionate to .vertline.X.vertline..sup.3 which, of course, is not cylindrical at all. In addition the loading technique produces some random warping because the loading is not determinate when the deflections are small ('1 micron).
A second type of device for adjusting the curvature of a light reflecting surface is described in an article entitled "three-actuator deformable water-cooled mirror" by Anthony Fuschetto the Perkin-Elmer Corporation published in OPTICAL ENGINEERING/March/April 1981/Vol. 20. No. 2. The device described there uses three piezoelectric stacks connected to six distinct points along the edges of a circular mirror. Each of these stacks applies a force between an associated pair of these points, generally parallel to the mirrored surface, thereby applying a bending moment to the mirror for bending the latter.
The Fuschetto approach just described is a more accurate way to obtain a cylindrical contour on a mirror for correcting for astigmatism than the approach illustrated in FIGS. 2 and 3. However, even the Fuschetto design does not provide for accurately uniformly contouring the mirrored surface along its entire extent. A primary reason for this is that the mirrored surface is arcuate (circular) and each piezoelectric stack concentrates its application of force to distinct points on the edge of the mirrored surface.